diff -r bea0c3841ced -r b4a47e8e80d1 src/convex.rs
--- a/src/convex.rs	Wed Sep 03 09:16:03 2025 -0500
+++ b/src/convex.rs	Wed Sep 03 09:52:30 2025 -0500
@@ -17,7 +17,7 @@
 ///
 /// TODO: should constrain `Mapping::Codomain` to implement a partial order,
 /// but this makes everything complicated with little benefit.
-pub trait ConvexMapping<Domain: Normed<F>, F: Num = f64>: Mapping<Domain, Codomain = F> {
+pub trait ConvexMapping<Domain: Space, F: Num = f64>: Mapping<Domain, Codomain = F> {
     /// Returns (a lower estimate of) the factor of strong convexity in the norm of `Domain`.
     fn factor_of_strong_convexity(&self) -> F {
         F::ZERO
@@ -42,7 +42,7 @@
 /// but a `Preconjugable` mapping has to be convex.
 pub trait Preconjugable<Domain, Predual, F: Num = f64>: ConvexMapping<Domain, F>
 where
-    Domain: Normed<F>,
+    Domain: Space,
     Predual: HasDual<F>,
 {
     type Preconjugate<'a>: Mapping<Predual, Codomain = F>
@@ -88,7 +88,7 @@
 
 impl<Domain, E, F> ConvexMapping<Domain, F> for NormMapping<F, E>
 where
-    Domain: Normed<F>,
+    Domain: Space,
     E: NormExponent,
     F: Float,
     Self: Mapping<Domain, Codomain = F>,
@@ -97,7 +97,8 @@
 
 impl<F, E, Domain> Mapping<Domain> for NormConstraint<F, E>
 where
-    Domain: Space + Norm<E, F>,
+    Domain: Space,
+    Domain::OwnedSpace: Norm<E, F>,
     F: Float,
     E: NormExponent,
 {
@@ -114,7 +115,7 @@
 
 impl<Domain, E, F> ConvexMapping<Domain, F> for NormConstraint<F, E>
 where
-    Domain: Normed<F>,
+    Domain: Space,
     E: NormExponent,
     F: Float,
     Self: Mapping<Domain, Codomain = F>,
@@ -125,7 +126,8 @@
 where
     E: HasDualExponent,
     F: Float,
-    Domain: HasDual<F> + Norm<E, F> + Normed<F>,
+    Domain: HasDual<F>,
+    Domain::OwnedSpace: Norm<E, F>,
     <Domain as HasDual<F>>::DualSpace: Norm<E::DualExp, F>,
 {
     type Conjugate<'a>
@@ -143,7 +145,8 @@
     C: Constant<Type = F>,
     E: HasDualExponent,
     F: Float,
-    Domain: HasDual<F> + Norm<E, F> + Space,
+    Domain: HasDual<F>,
+    Domain::OwnedSpace: Norm<E, F>,
     <Domain as HasDual<F>>::DualSpace: Norm<E::DualExp, F>,
 {
     type Conjugate<'a>
@@ -161,7 +164,8 @@
 
 impl<Domain, E, F> Prox<Domain> for NormConstraint<F, E>
 where
-    Domain: Space + Norm<E, F>,
+    Domain: Space,
+    Domain::OwnedSpace: Norm<E, F>,
     E: NormExponent,
     F: Float,
     NormProjection<F, E>: Mapping<Domain, Codomain = Domain::OwnedSpace>,
@@ -201,8 +205,8 @@
 
 impl<F, E, Domain> Mapping<Domain> for NormProjection<F, E>
 where
-    Domain: Normed<F> + Projection<F, E>,
-    Domain::OwnedSpace: ClosedSpace,
+    Domain: Space,
+    Domain::OwnedSpace: ClosedSpace + Projection<F, E>,
     F: Float,
     E: NormExponent,
 {
@@ -232,7 +236,7 @@
     }
 }
 
-impl<Domain: Normed<F>, F: Float> ConvexMapping<Domain, F> for Zero<Domain, F> {}
+impl<Domain: Space, F: Float> ConvexMapping<Domain, F> for Zero<Domain, F> {}
 
 impl<Domain: HasDual<F>, F: Float> Conjugable<Domain, F> for Zero<Domain, F> {
     type Conjugate<'a>
@@ -249,7 +253,7 @@
 impl<Domain, Predual, F: Float> Preconjugable<Domain, Predual, F> for Zero<Domain, F>
 where
     Domain: Normed<F>,
-    Predual: HasDual<F>,
+    Predual: HasDual<F, Owned = Predual>,
 {
     type Preconjugate<'a>
         = ZeroIndicator<Predual, F>
@@ -284,7 +288,12 @@
     }
 }
 
-impl<Domain: Normed<F>, F: Float> Mapping<Domain> for ZeroIndicator<Domain, F> {
+impl<Domain, F> Mapping<Domain> for ZeroIndicator<Domain, F>
+where
+    F: Float,
+    Domain: Space,
+    Domain::OwnedSpace: Normed<F>,
+{
     type Codomain = F;
 
     /// Compute the value of `self` at `x`.
@@ -293,13 +302,21 @@
     }
 }
 
-impl<Domain: Normed<F>, F: Float> ConvexMapping<Domain, F> for ZeroIndicator<Domain, F> {
+impl<Domain, F: Float> ConvexMapping<Domain, F> for ZeroIndicator<Domain, F>
+where
+    Domain: Space,
+    Domain::OwnedSpace: Normed<F>,
+{
     fn factor_of_strong_convexity(&self) -> F {
         F::INFINITY
     }
 }
 
-impl<Domain: HasDual<F>, F: Float> Conjugable<Domain, F> for ZeroIndicator<Domain, F> {
+impl<Domain, F: Float> Conjugable<Domain, F> for ZeroIndicator<Domain, F>
+where
+    Domain: HasDual<F>,
+    Domain::Owned: Normed<F>,
+{
     type Conjugate<'a>
         = Zero<Domain::DualSpace, F>
     where
@@ -313,7 +330,8 @@
 
 impl<Domain, Predual, F: Float> Preconjugable<Domain, Predual, F> for ZeroIndicator<Domain, F>
 where
-    Domain: Normed<F>,
+    Domain: Space,
+    Domain::OwnedSpace: Normed<F>,
     Predual: HasDual<F>,
 {
     type Preconjugate<'a>